Gas Turbine Combustor: Modelling and Optimization

This paper presents an experimental and numerical study of the flow field and heat release (HRL) zone of a six-nozzle FLOX®-based combustor at atmospheric pressure. The combustor is suitable for the use in a micro gas turbine (MGT) based combined heat and power (CHP) system with an electrical power output of 3 kW. The velocity field was measured using stereoscopic particle image velocimetry (PIV). The heat release zone was visualized by OH*-chemiluminescence (OH* CL) and the flame front by OH planar laser-induced fluorescence (OH PLIF). The results are compared with CFD simulations to evaluate the quality of the applied numerical turbulence and combustion models. The simulations were performed using Reynolds-averaged Navier-Stokes equations in combination with the k-ω-SST-turbulence model. Since the FLOX®-based combustion is dominated by chemical kinetics, a reaction mechanism with detailed chemistry, including 22 species and 104 reactions (DRM22), has been chosen. To cover the turbulence-chemistry interaction, an assumed probability density function (PDF) approach for species and temperature was used. Except for minor discrapancies in the flow field, the results show that the applied models are suitable for the design process of the combustor. In terms of the location of the heat release zone, it is necessary to consider possible heat losses, especially at lean operating conditions with a distributed heat release zone.

In this paper, a new "presumed" Probability Density Function (PDF) approach coupled with a Lagrangian tracking method is proposed for turbulent combustion modeling. The test and the investigation of the model are conducted by comparing the model results with DNS data for a premixed flame subjected in a decaying turbulent field. The newly constructed PDF, which incorporates the instantaneous chemical reaction term, demonstrates consistent improvement over conventional assumed PDF models. It has been found that the time evolution of the mean scalar, the variance and the mean reaction rate are strongly influenced by a parameter deduced by a Lagrangian equation which takes into account explicitly the local reaction rate. Tests have been performed for a moderate Damk?hler number, and it is expected the model may cover a broader range of Damk?hler number. The comparison with the DNS data demonstrates that the proposed model may be promising and affordable for implementation in a moment-equation solver.

Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities: A Probability Density Function Approach

The present work is concerned with the ability of a two-equation turbulence model (K-epsilon) of predicting accurately the mixing parameters at the outlet of an annular gas turbine combustor. A comparison between numerical and experimental results is presented with attention paid to numerical accuracy and boundary condition sensitivity. A numerical grid with 36,000 nodes was needed to resolve the flow inside a 7.5-deg annular sector. It was found that an insufficient number of grid nodes led to the underprediction of the streamwise vorticity and a different flow pattern in the wake and downstream of the jets. Two basic sets of calculations with constant and variable density are included. The calculations could predict the general features of the flow, but evidenced lower levels of mixing compared to the experiments, even with a reduction of the turbulent Prandtl number from 0.9 to 0.5. 22 refs.

A method is presented for computing steady two-phase turbulent combusting flow in a gas turbine combustor. The gas phase equations are solved in an Eulerian frame of reference. The two-phase calculations are performed by using a liquid droplet spray combustion model and treating the motion of the evaporating fuel droplets in a Lagrangian frame of reference. The numerical algorithm employs nonorthogonal curvilinear coordinates, a multigrid iterative solution procedure, the standard k-ε turbulence model, and a combustion model comprising an assumed shape probability density function and the conserved scalar formulation. The trajectory computation of the fuel provides the source terms for all the gas phase equations. This two-phase model was applied to a real piece of combustion hardware in the form of a modern GE/SNECMA single annular CFM56 turbofan engine combustor. For the purposes of comparison, calculations were also performed by treating the fuel as a single gaseous phase. The effect on the solution of two extreme situations of the fuel as a gas and initially as a liquid was examined. The distribution of the velocity field and the conserved scalar within the combustor, as well as the distribution of the temperature field in the reaction zone and in the exhaust, were all predicted with the combustor operating both at high-power and low-power (ground idle) conditions. The calculated exit gas temperature was compared with test rig measurements. Under both low and high-power conditions, the temperature appeared to show an improved agreement with the measured data when the calculations were performed with the spray model as compared to a single-phase calculation.

LES/PDF based modeling of soot–turbulence interactions in turbulent flames

LES-based Eulerian PDF approach for the simulation of scramjet combustors

Transported probability density function modelling of the vapour phase of an n-heptane jet at diesel engine conditions

Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems: A Probability Density Function Approach

<div class="htmlview paragraph">A gas turbine combustion system is an embodiment of all complexities that engineering equipment can have. The flow is three dimensional, swirling, turbulent, two phase and reacting. The design and development of combustors, until recent past, was an art than science. If one takes the route of development through experiments, it is quite time consuming and costly. Compared to the other two components viz., compressor and turbine, the combustion system is not yet completely amenable to mathematical analysis.</div> <div class="htmlview paragraph">A gas turbine combustor is both geometrically and fluid dynamically quite complex. The major challenge a combustion engineer faces is the space constraint. As the combustion chamber is sandwiched between compressor and turbine there is a limitation on the available space. The critical design aspect is in facing the aerodynamic challenges with minimum pressure drop. Accurate mathematical analysis of such a system is next to impossible. However, because of the advent of fast digital computers now a days it has become possible to model both geometrical and fluid dynamics aspects of a combustor using computers. The advances in modeling techniques have evolved over a period of time. Commercial codes are now available which has made the task comparatively easier.</div> <div class="htmlview paragraph">The present study is an attempt to predict numerically the entire flow field from compressor exit to combustor exit. The novelty of this study is in the modeling of all the holes amounting to 1700 in all, with appropriate grid distribution. The inclusion of conjugate heat transfer was a challenge. The appropriate governing equations are solved using RNG k- ε turbulence model for non-reacting flows whereas for reacting flows with heat transfer only k- ε is used. Eighteen million grid cells are employed to incorporate holes, fuel injection, combustion and conjugate heat transfer. The combustion is modeled using prePDF combustion model. It took nearly 2000 hrs of CPU time in a sun server (4 node machine) with the main memory of 128GB.</div> <div class="htmlview paragraph">Non-reacting flow analysis of the combustor reveals that size of the holes in dome and flare has little effect on the total pressure loss. However, increase in inlet velocity by 37% increases the total pressure loss by 86% across combustor. An Injection velocity of 75 m/s is found to give a good combustion characteristic inside the flame tube. Therefore conjugate heat transfer study is carried out with this injection velocity. Temperature distribution inside the flame tube and heat transfer through flare and the hot streaks in the liner wall are studied. Flare (without holes) is subjected to higher temperature (2480K) as it is found to be close to the primary combustion zone. It is also inferred from the study that the presence of holes protects the dome and flare from high temperature due to combustion. Holes in dome and flare are found to reduce the maximum temperature by 350K.</div> <div class="htmlview paragraph">The predicted results provide a complete picture of flow field as well as temperature distribution. Pressure drop and pattern factor have been evaluated. Even \cf4 cf4 tho\cf4 cf1 ugh this particular study has not been validated, the code has already been validated for a different geometry given in reference [<span class="xref">13</span>].\cf4 cf4 It\cf4 cf1 is gratifying to note that the present numerical procedure has predicted reasonable and plausible results.\cf4 cf4 It\cf4 cf1 \cf4 cf4 may be\cf4 cf1 concluded that CFD can \cf4 cf4 be \cf4 cf1 used with reasonable confidence, for the design and development of gas turbine combustion system. However, to enhance the confidence, validation must \cf4 cf4 be \cf4 cf1 attempted in future studies.</div>

Comparison of transported scalar PDF and velocity-scalar PDF approaches to ‘Delft flame III’

The tabulated premixed conditional moment closure (T-PCMC) method has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes in Reynolds-averaged Navier–Stokes (RANS) environment by Martin et al. (2013, “Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method,” ASME Paper No. GT2013-95092). Here, the premixed conditional moment closure (PCMC) method is extended to large eddy simulation (LES). The new model is validated with the turbulent, enclosed reacting methane backward facing step data from El Banhawy et al. (1983, “Premixed, Turbulent Combustion of a Sudden-Expansion Flow,” Combust. Flame, 50, pp. 153–165). The experimental data have a rectangular test section at atmospheric pressure and temperature with an inlet velocity of 10.5 m/s and an equivalence ratio of 0.9 for two different step heights. Contours of major species, velocity, and temperature are provided. The T-PCMC model falls into the class of table lookup turbulent combustion models in which the combustion model is solved offline over a range of conditions and stored in a table that is accessed by the computational fluid dynamic (CFD) code using three controlling variables: the reaction progress variable (RPV), variance, and local scalar dissipation rate. The local scalar dissipation rate is used to account for the affects of the small-scale mixing on the reaction rates. A presumed shape beta function probability density function (PDF) is used to account for the effects of subgrid scale (SGS) turbulence on the reactions. SGS models are incorporated for the scalar dissipation and variance. The open source CFD code OpenFOAM is used with the compressible Smagorinsky LES model. Velocity, temperature, and major species are compared to the experimental data. Once validated, this low “runtime” CFD turbulent combustion model will have great utility for designing the next generation of lean premixed (LPM) gas turbine combustors.

Non-Linear Combustion Instabilities in Annular Gas-Turbine Combustors

Assumed PDF turbulence-chemistry closure with temperature-composition correlations

This study investigates the performance and the conditions under which flameless oxidation can be achieved for a given annular adiabatic combustor. Numerical modelling of velocity, temperature and species fields are performed for different flow configurations of air and methane streams injected into a proposed design of a gas-turbine combustor. Parametric analysis was performed by systematically varying several parameters: radius of a recirculation zone, radius of the combustor, location of air and fuel ports, air and fuel velocities magnitudes and injection angles. The analysis was performed initially using a three-step global chemistry model to identify a design (geometry and operating conditions) that yield flameless combustion regime. The selected design was then modelled using a skeletal (46 reactions) and a detailed (309 reactions) chemical kinetics mechanism. The k–ε turbulence model was used in the most calculations. Overall, similar qualitative flow, temperature, and species patterns were predicted by both kinetics models; however the detailed mechanism provides quantitatively more realistic predictions. An optimal flow configuration was achieved with exhaust NOx emissions of < 7.5 ppm, CO < 35ppm, and a pressure-drop < 5%, hence meeting the design criteria for gas turbine engines. This study demonstrates the feasibility of achieving ultra-low NOx and CO emissions utilising a flameless oxidation regime.